A publication of the Theta Foundation.
2007; 356 pp; hardcover
ISBN-10: 973-87899-0-7
ISBN-13: 978-973-87899-0-6
The volume is a careful selection of peer-reviewed papers in operator theory, structured matrices, and dilations, dedicated to Tiberiu Constantinescu, a prominent mathematician in the field.
The extensive survey of J. W. Helton and M. Putinar on positive polynomials, spectral theorem, and optimization is a pioneering essay that, under the unifying concept of positivity, brings together ideas from algebra, algebraic geometry, complex analysis, control theory, mathematical logic, and operator theory.
The other research papers deal with recent advances in the following areas:
multivariable operator theory
interpolation and moment problems
perturbation theory
composition operators
matrix completion problems
systems theory
A publication of the Theta Foundation. Distributed worldwide, except in Romania, by the AMS.
Readership
Graduate students and research mathematicians interested in analysis.
Table of Contents
D. Alpay, R. W. Buursema, A. Dijksma, and H. Langer -- The combined moment and interpolation problem for Nevanlinna functions
D. Z. Arov and O. Staffans -- State/signal linear time-invariant systems theory, Part III: Transmission and impedance representations of discrete time systems
M. Bakonyi and D. Timotin -- The central completion of a positive block operator matrix
J. A. Ball, V. Bolotnikov, and Q. Fang -- Schur-class multipliers on the Fock space: de Branges-Rovnyak reproducing kernel spaces and transfer-function realizations
H. Bercovici and W. S. Li -- Invariant subspaces with extremal structure
for operators of class C_0
A. K. Beros and D. Sarason -- Composition operators and change of variable in one real dimension
P. A. Cojuhari -- On the spectrum of a class of block Jacobi matrices
M. A. Dritschel and S. McCullough -- Test functions, kernels, realizations and interpolation
Y. Hachez and H. J. Woerdeman -- The Fischer-Frobenius transformation and outer factorization
S. Hassi, H. S. V. de Snoo, A. E. Sterk, and H. Winkler -- Finite-dimensional graph perturbations of selfadjoint Sturm-Liouville operators
J. W. Helton and M. Putinar -- Positive polynomials in scalar and matrix variables, the spectral theorem, and optimization
G. Popescu -- Von Neumann inequality on noncommutative domains
J. Rovnyak and L. A. Sakhnovich -- Interpolation problems for matrix integro-differential operators with difference kernels and with a finite number of negative squares
M. C. Tseng and V. Ramakrishna -- Dilation theoretic parametrizations of positive matrices with applications to quantum information
DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Volume: 73
2008; 165 pp; hardcover
ISBN-10: 0-8218-3752-4
ISBN-13: 978-0-8218-3752-8
Expected publication date is February 22, 2008.
This book comprises a collection of articles stemming from a DIMACS Working Group and DIMACS Workshop on Theoretical Advances in Information Recording held at Rutgers University, Piscataway, NJ. Written by leading researchers in information theory and data storage technology, the articles address problems related to the efficient and reliable storage of information in devices based upon novel optical, magnetic, and biological recording mechanisms.
The primary focus of the articles is on signal processing and coding techniques applicable to exploratory technologies being considered for future generations of storage devices, including two-dimensional optical storage (TwoDOS), heat-assisted magnetic recording (HAMR), and volumetric macro-molecular data storage. Specific topics addressed include channel equalization, timing recovery, data detection, modulation coding, and error control coding. Several articles explore the emerging connections between data storage, information theory, and the storage and processing of genetic information in living cells. Articles in the volume also illustrate the broader applicability of fundamental advances in information theory that have arisen in the context of information storage technology.
The volume is suitable for graduate students and research scientists interested in applications of information theory, communication theory, and coding theory to man-made and natural data storage systems.
Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).
Readership
Graduate students and research mathematicians interested in mathematical problems of information theory and data storage.
Table of Contents
W. M. J. Coene and A. H. J. Immink -- Modulation coding for a two-dimensional optical storage channel
R. Radhakrishnan, B. Vasic, F. Erden, and C. He -- Characterization of heat-assisted magnetic recording channels
A. R. Nayak, J. R. Barry, and S. W. McLaughlin -- Cramer-Rao bound for timing recovery on channels with inter-symbol interference
M. Mansuripur and P. Khulbe -- Macro-molecular data storage with petabyte/cm^3
density, highly parallel read/write operations, and genuine 3D storage
capability
G. Battail -- Can we explain the faithful communication of genetic information?
O. Milenkovic -- Data storage and processing in cells: An information theoretic approach
N. Kashyap and P. H. Siegel -- Ghostbusting: Coding for optical communications
Mathematical Surveys and Monographs, Volume: 146
2008; 187 pp; hardcover
ISBN-10: 0-8218-4402-4
ISBN-13: 978-0-8218-4402-1
Expected publication date is April 16, 2008.
The study of positive polynomials brings together algebra, geometry and analysis. The subject is of fundamental importance in real algebraic geometry, when studying the properties of objects defined by polynomial inequalities. Hilbert's 17th problem and its solution in the first half of the 20th century were landmarks in the early days of the subject. More recently, new connections to the moment problem and to polynomial optimization have been discovered. The moment problem relates linear maps on the multidimensional polynomial ring to positive Borel measures.
This book provides an elementary introduction to positive polynomials and
sums of squares, the relationship to the moment problem, and the application
to polynomial optimization. The focus is on the exciting new developments
that have taken place in the last 15 years, arising out of Schmudgen's
solution to the moment problem in the compact case in 1991. The book is
accessible to a well-motivated student at the beginning graduate level.
The objects being dealt with are concrete and down-to-earth, namely polynomials
in n variables with real coefficients, and many examples are included.
Proofs are presented as clearly and as simply as possible. Various new,
simpler proofs appear in the book for the first time. Abstraction is employed
only when it serves a useful purpose, but, at the same time, enough abstraction
is included to allow the reader easy access to the literature. The book
should be essential reading for any beginning student in the area.
Readership
Graduate students and research mathematicans interested in positive polynomials in algebra, geometry, and analysis; semialgebraic geometry.
Table of Contents
Preliminaries
Positive polynomials and sums of squares
Krivine's Positivstellensatz
The moment problem
Non-compact case
Archimedean T-modules
Schmudgen's Positivstellensatz
Putinar's question
Weak isotropy of quadratic forms
Scheiderer's local-global principle
Semidefinite programming and optimization
Appendix 1: Tarski-Seidenberg theorem
Appendix 2: Algebraic sets
Bibliography
Contemporary Mathematics, Volume: 449
2008; 446 pp; softcover
ISBN-10: 0-8218-4225-0
ISBN-13: 978-0-8218-4225-6
George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics.
Topics examined here include recent results on induced representations, virtual groups, the Mackey Machine and crossed products, representations of Baumslag-Solitar groups, the Radon transform and the heat equation, groupoids in the study of wavelets, and quantum theory. The in-depth historical surveys of Mackey's work on representation theory, ergodic theory, and physics, together with recent developments inspired by his fundamental work will be of considerable interest to both graduate students and researchers alike.
Readership
Graduate students and research mathematicians interested in ergodic theory and mathematicial physics.
Table of Contents
R. S. Doran and A. Ramsay -- George Mackey 1916-2006
S. Adams -- Decay to zero of matrix coefficients at adjoint infinity
J. Arthur -- Induced representations, intertwining operators and transfer
L. G. Brown -- MASA's and certain type I closed faces of C*-algebras
D. E. Dutkay and P. E. T. Jorgensen -- A duality approach to representations of Baumslag-Solitar groups
S. Echterhoff and D. P. Williams -- The Mackey machine for crossed products: Inducing primitive ideals
E. G. Effros -- Classifying the unclassifiables
N. Higson -- The Mackey analogy and K-theory
R. E. Howe -- Some recent applications of induced representations
M. Ionescu and P. S. Muhly -- Groupoid methods in wavelet analysis
A. Jaffe -- Quantum theory and relativity
A. A. Kirillov -- Thoughts about George Mackey and his imprimitivity theorem
C. C. Moore -- Virtual groups 45 years later
F. Murnaghan -- Spherical characters: The supercuspidal case
G. Olafsson and H. Schlichtkrull -- Representation theory, radon transform and the heat equation on a Riemannian symmetric space
J. A. Packer -- Projective representations and the Mackey obstruction-A survey
A. Ramsay -- Virtual groups for group representations
M. A. Rieffel -- A global view of equivariant vector bundles and Dirac operators on some compact homogeneous spaces
V. S. Varadarajan -- George Mackey and his work on representation theory and foundations of physics
Contemporary Mathematics, Volume: 450
2008; 311 pp; softcover
ISBN-10: 0-8218-4423-7
ISBN-13: 978-0-8218-4423-6
Expected publication date is February 24, 2008.
This volume is a collection of articles by speakers at the conference "Poisson 2006: Poisson Geometry in Mathematics and Physics", which was held June 5-9, 2006, in Tokyo, Japan. Poisson 2006 was the fifth in a series of international conferences on Poisson geometry that are held once every two years. The aim of these conferences is to bring together mathematicians and mathematical physicists who work in diverse areas but have common interests in Poisson geometry. The program for Poisson 2006 was remarkable for the overlap of topics that included deformation quantization, generalized complex structures, differentiable stacks, normal forms, and group-valued moment maps and reduction. The articles represent current research in Poisson geometry and should be valuable to anyone interested in Poisson geometry, symplectic geometry, and mathematical physics. This volume also contains lectures by the principal speakers of the three-day school held at Keio University that preceded Poisson 2006.
Readership
Graduate students and research mathematicians interested in Symplectic and Poisson geometry, deformation quantization, and mathematical physics.
Table of Contents
P. Bieliavsky, L. Claessens, D. Sternheimer, and Y. Voglaire -- Quantized anti de Sitter spaces and non-formal deformation quantizations of symplectic symmetric spaces
C. Blohmann and A. Weinstein -- Group-like objects in Poisson geometry and algebra
O. Brahic and R. L. Fernandes -- Poisson fibrations and fibered symplectic groupoids
H. Bursztyn, G. R. Cavalcanti, and M. Gualtieri -- Generalized Kahler and hyper-Kahler quotients
A. S. Cattaneo -- Deformation quantization and reduction
J.-P. Dufour -- Examples of higher order stable singularities of Poisson structures
F. Gay-Balmaz and T. S. Ratiu -- Poisson reduction and the Hamiltonian structure of the Euler-Yang-Mills equations
T. S. Holm -- Orbifold cohomology of abelian symplectic reductions and the case of weighted projective spaces
N. IKEDA -- Deformation of graded Poisson (Batalin-Vilkovisky) structures
A. V. Karabegov -- Deformation quantization of a Kahler-Poisson structure vanishing on a Levi nondegenerate hypersurface
J.-H. Lu -- A note on Poisson homogeneous spaces
E. Meinrenken -- Lectures on pure spinors and moment maps
S. A. Merkulov -- Lectures on props, Poisson geometry and deformation quantization
P. Schapira -- Deformation quantization modules on complex symplectic manifolds
M. Van den Bergh -- Non-commutative quasi-Hamiltonian spaces
S. Waldmann -- Locally noncommutative space-times